Methods have been developed for automated testing of web pages, web sites, and other types of information displayed to user on display devices of computer systems and other electronic devices and systems. In many cases, a test administrator my wish to know how long the test will take to run in order to achieve a specified significance level. A test-duration estimation may assist the test administrator or automated-testing-system user to choose a test design that best satisfies business requirements and that best manages the resources necessary to complete the test. Usually the test duration estimate is based on user-supplied information regarding a control-conversion rate. As an automated test is executed and more data is received, it could be inferred that a test duration estimate could be made with greater accuracy to facilitate decisions regarding when to terminate the test. Stopping a test run too early may result in a subsequent analysis of test data giving incorrect results. On the other hand, running a test longer than necessary for a pre-specified significance level unnecessarily consumes resources and delays implementation of improvements indicated by results of the test.